The release of Xanathar's Guide to Everything includes additional rules for things under Chapter 2 Dungeon Master's Tools.
Are those rules official updates/clarifications to the Core Rules or are they considered Optional/Variants that you a DM can utilize?
In the introduction to the book, the authors state (emphasis mine):
The first major rules expansion to the fifth edition of D&D, Xanathar’s Guide to Everything provides a wealth of new options for the game
Written for both players and Dungeon Masters, this source offers options to enhance campaigns in any world, whether you’re adventuring in the Forgotten Realms, another official D&D setting, or a world of your own creation. The options here build on the official rules contained within the Player’s Handbook, the Monster Manual, and the Dungeon Master’s Guide. Think of this source as the companion to those volumes. It builds on their foundation, exploring pathways first laid in those publications. Nothing herein is required for a D&D campaign — this is not a fourth core rulebook — but we hope it will provide you new ways to enjoy the game.
The introduction to Chapter 2 also states (emphasis mine):
It gives you new rules options, as well as some refined tools for creating and running adventures and campaigns. It is a supplement to the tools and advice offered in the Dungeon Master’s Guide.
The chapter opens with optional rules meant to help you run certain parts of the game more smoothly.
The material in this chapter is meant to make your life easier. Ignore anything you find here that doesn’t help you, and don’t hesitate to customize the things that you do use.
It then goes on to say:
The chapter opens with optional rules meant to help you run certain parts of the game more smoothly. The chapter then goes into greater depth on several topics — encounter building, random encounters, traps, magic items, and downtime — which largely relate to how you create and stage your adventures.
This seems to suggest that the content prior to Encounter Building all falls under optional rules, but the 'greater depth' starting at that point suggests those are clarifications.
In total, it's fairly unclear, and each table may need to decide what they want to do with the content in Chapter 2.
Not all of Xanathar's content in Chapter 2 are of the Optional/Variant type.
When the book mirrors something that is an official Core rule errata, update, answer, then those ARE official Core Rule updates/clarifications. Unfortunately, there is no simple way to determine which rules discussed have that mirror. The Ten Rules To Remember on Page 5 does seem to be one of these mirrors and should be considered Core Rules Clarifications.
